# Entropy production and thermodynamics of information under protocol constraints

We investigate bounds on the entropy production (EP) and extractable work involved in transforming a system from some initial distribution p to some final distribution p', given the driving protocol constraint that the dynamical generators belong to some fixed set. We first show that, for any operator ϕ over distributions that (1) obeys the Pythagorean theorem from information geometry and (2) commutes with the set of available dynamical generators, the contraction of KL divergence D(p‖ϕ(p))-D(p' ‖ϕ(p')) provides a non-negative lower bound on EP. We also derive a bound on extractable work, as well as a decomposition of the non-equilibrium free energy into an "accessible free energy" (which can be extracted as work) and "inaccessible free energy" (which must be dissipated as EP). We use our general results to derive bounds on EP and work that reflect symmetry, modularity, and coarse-graining constraints. We also use our results to decompose the information acquired in a measurement of a system into "accessible information" (which can be used to extract work from the system) and "inaccessible information" (which cannot be used to extract work from the system). Our approach is demonstrated on several examples, including different kinds of Szilard boxes and discrete-state master equations.

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